"They must apply to everyone, or they mean nothing!" strikes me as a misplaced rhetorical flourish. It sounds exciting and forceful, but it doesn't fit the situation.

First of all, it seems meant to suggest the Declaration of Independence (We hold these truths to be self-evident, that all men are created equal...), not the Preamble to the Constitution that Kirk just recited.

Second, taking Kirk literally implies that the Yangs now have a moral duty to conquer all Comb territory and annex it under the government defined in the Yang Constitution. And that doesn't sit right as a moral imperative.